Ella deposited $\$2500$ into a savings account. The relationship between the time, $t$, in years, since the account was first opened, and Ella's account balance, $B(t)$, in dollars, is modeled by the following function. $B(t)=2500 \cdot e^{0.025t}$ What will the balance of Ella's savings account be after $4$ years? Round your answer, if necessary, to the nearest hundredth. $\$$
Thinking about the problem We want to find the balance in Ella's savings account after $4$ years. In other words, we are given a $t$ value of $4$ years and want to find the balance associated with that input, or $B(4)$. To do this, we can substitute ${4}$ in for $ t$ and evaluate. $B({4})=2500 \cdot e^{0.025({4})}$ Evaluating the expression We can use a calculator to evaluate the expression. The answer is shown below. $\begin{aligned}B(4)&=2500\cdot e^{{0.025(4)}}\\\\ &=2500\cdot e^{{0.1}}\\\\ &\approx2762.93\\\\ \end{aligned}$ In $4$ years, the balance in Ella's savings account will be about $\$2762.93$.